An indicator function of the set A is the function on N given by if w E A lo if w € A so that 1, indicates whether A occurs. Operations on indicator functions are equivalent to set [1 1¼(w) = operations on events 1AUB = max{14, 1g} 1ang = min{1,, 1g} = 1,1, 1,c = 1 – 1, 1aar = |1, – 1g|

Q: Use the factorization A = PDP Ak= - 7 40 - 2 11 = 45 1 1 1 01 30 to compute A I -1 5 1 - 4 1 where k…

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Q: 16 M = 7 -5 Find formulas for the entries of M", where n is a positive integer. M" =

A: We have to find the entries of matrix Mn.

Q: In the POW A Digital Proof, you had to place digits in five boxes in a way that satisfied certain…

A: We have to label the given boxes where representation is not unique i.e., we got many…

Q: [1+6n A" 7 4 4n -9 -5 -9n 1-6n | If , show that for every n natural number.

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Q: what is an algebra expresion

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Q: In Exercises 1-17 find a particular solution. 2. у" + Зу' + у %3 (2 — 6х) сos х — 9 sin x

A: The second order non homogeneous ordinary differential equation y’’ + 3 y’ + y = (2 – 6x) cos x – 9…

Q: In how many ways can ten keys be put on a key ring? 10! 10!-10 10!/2 2-10! 10!/10

A: Answer is 10!/10. Last option is correct.

Q: Jeremiah has six boxes of six different sizes. Four boxes are taken at a time and arranged in…

A: Given that, Jeremiah has six boxes of six different sizes. Four boxes are taken at a time and…

Q: Any whole number is divisible by 3 if and only if the sum of its digits is divisible by 3 TRUE FALSE

A: We have to state that the given statement is true or false.   Any whole number is divisible by 3 if…

Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

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Q: Find the eighth row in Pascal's triangle. List the entries of the eighth row in Pascal's triangle in…

A: Solution-: We find the 8th row of pascal's triangle=?

Q: Solve the system x = y = Z= 2x +2y x -2= 2 -3y +2= -28 +y 4 -X =

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Q: The sum of the squares of the first 5 fibonacci terms, check and prove

A: Fibonnaci Sequence is: 1,1,2,3,5,8,13,21,34,55,89,... (That is, each term of the sequence is the sum…

Q: 12 = -3 (mod 5) Select one: True False

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Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

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Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: 24 Ct -3)²

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Q: If a = 17 (mod 3), then what is the remainder of a when divided by 3? Enter the numerical value.

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Q: 6. Solve the equation x + 3x + 17 = 0 (mod 21)

A: The Chinese reminder theorem:                    Let p and q are coprime. Then the system equations…

Q: Find all solutions of the congmonce 12X = 3 (mod 45)

A: The given problem is to find the all solutions for the given congruence equation.Given congruence…

Q: I have a message 2,3,6,5 (mod.7),  I will find a check digit by multiplying the first and third…

A: Here, First number= 2 Second number =3 Third number= 6 Fourth number= 5

Q: مال ق (3+یع

A: (d) Given that                                                I=∫(2x+3)2xdx

Q: Solve x2+3x+2 is congruent to 0 (mod 55)

A: 55=5×11 and gcd(5,11)=1, hence they are co-prime.The given system of equation x2+3x+2≡0mod 55 is…

Q: A number with 4 digits is formed from the digits 0, 3, 6, 7, 9 without repetition. How many numbers…

A: Total numbers = 5 Since the 6 and 7 are placed next to each other consider them as a single number.…

Q: Problem 1. An egg was put in a pot filled with hot water, in order to warm it. Suppose that at the…

A: Since you have posted a question with multiple sub-parts, we will solve the first subpart for you…

Q: Prove that if the sum of the digits is subtracted from a natural number, then the result is…

A: let us assume the number to be three digit number xyz therefore, xyz=100x+10y+z sum of digits will…

Q: can you write this all on paper if possible including all parts that have been answered

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Q: Write down the 7th row of Pascal's Triangle.

A: We have to find the 7th row of Pascal's Triangle

Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: How many real four digit numbers (they can not start with zero) can be formed from digits 0, 1, 2,…

A: Given digits is 0,1,2,3,4,5,6Total no.of digits = 7

Q: 7 4 3 find Jordan form -2 12 -2 9 -4 9

A: We have to find the Jordan canonical form of the given Matrix.

Q: If p, q, r are prime numbers such that pqr = 19(p + q + r) then the value of 2(p + q + r) is

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Q: Prove {12a + 4b : a and b are integers} = {4c : c is an integer}

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Q: 237 (mod 10)

A: We use the definition of a (mod b) to find the value of 237 (mod 10).

Q: Find the 66th term of the triangular numbers {1, 3, 6, …}.

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